具黏弹性项的双曲方程解的存在性与衰减估计  

Existence and decay estimation of solution for hyperbolic equation with viscoelastic term

作　　者：范鑫宇 高艳超 FAN Xinyu;GAO Yanchao(School of Mathematics and Statistics,Changchun University of Science and Technology,Changchun 130013,Jilin,China)

机构地区：[1]长春理工大学数学与统计学院,吉林长春130013

出　　处：《山东大学学报(理学版)》2025年第2期63-71,84,共10页Journal of Shandong University(Natural Science)

基　　金：吉林省自然科学基金资助项目(YDZJ202201ZYTS584)。

摘　　要：研究了一类具黏弹性项的四阶双曲方程的初边值问题。利用Galerkin方法得到了弱解的局部存在性,利用位势井方法证明了弱解的整体存在性,并给出了整体解的衰减估计。The initial boundary value problem of a class of fourth order hyperbolic equation with viscoelastic term is studied.The local existence of the weak solution is obtained by using Galerkin method.Then the global existence of the weak solution is proved using the potential well method,and the decay estimate of the global solution is given.

关 键 词：黏弹性项 位势井 四阶双曲方程 衰减估计 

分 类 号：O175.27[理学—数学]